Examples on 45-degree Angle

Example 1: Finding the missing side length in a 45-45-90 triangle. If one leg of a 45-45-90 triangle measures 6 cm, what is the length of the hypotenuse?

Solution:

Since the leg is 6 cm, the hypotenuse

= 6 cm × √2

= 8.49 cm (approximately)

Example 2: Finding the degree measure of an angle based on its position in a shape. All four angles in a rectangle measure 90 degrees. If we draw a diagonal line dividing the rectangle into two congruent right triangles, what is the measure of each of the angles where the diagonal line meets the rectangle’s sides?

Solution:

By dividing the rectangle diagonally, we create two 45-45-90 triangles.

Because each triangle has one right angle (90 degrees), the two remaining angles must add up to the remaining 90 degrees (since the angles in a triangle sum to 180 degrees).

So, each of the angles where the diagonal meets the sides of the rectangle measures

90 degrees / 2 = 45 degrees

Example 3: Using a 45-degree angle to solve for an unknown distance. You are standing next to a building. You look up and see the top of the building at a 45-degree angle. You are 10 meters away from the base of the building, and your eye level is 1.5 meters from the ground. How tall is the building?

Solution:

This situation creates a 45-45-90 triangle, where the distance from you to the building (10 meters) is one leg and the unknown building height is the other leg.

Distance from your eye to the top of the building (what we want to find) is the hypotenuse. Since the legs in a 45-45-90 triangle are congruent the building height is also 10 meters.

Then, to find the total height from the ground to the top of the building we add the height of your eye level:

10 meters (building height) + 1.5 meters (eye level)

= 11.5 meters

45-degree angle is a fundamental concept in geometry and trigonometry. An angle is a form of geometrical shape constructed by joining two rays to each other at their endpoints. The two lines joined together are called the arms of the angle.

A 45-degree angle is exactly half of a right angle, which measures 90 degrees. Two 45-degree angles placed together form a right angle. In degrees, a 45-degree angle is 45/360 of a complete circle since its measure is between 0 and 90 degrees, a 45-degree angle is classified as an acute angle.

In this article, we will learn about, a 45-degree angle, how to draw a 45-degree angle using a compass and protractor, the properties of a 45-degree angle trigonometric values of a 45-degree angle and others in detail.